Enumeration of connected feedforward networks

Abstract. In their seminal work, Erdős and Rényi [3] uncovered a sharp transition in the size of the largest connected component of random graphs. Here, we consider feedforward networks which have important applications in artificial intelligence and sensory neural networks [9], [13]. We obtain generating functions for both the total number of feedforward networks and the number of connected feedforward networks as well as an asymptotic expression for the total number of feedforward networks. Moreover, considering a random family of feedforward networks, we uncover a sharp threshold in their probability of being connected.